Supplementary Information Solvation Free Energies and Hydration Structure of N-methyl-p-nitroaniline Alauddin Ahmed and Stanley I. Sandler † Department of Chemical Engineering and Biomolecular Engineering, University of Delaware, Newark, DE 19716 †Author to whom correspondence should be addressed (sandler@udel.edu) This PDF file includes Force Field Parameters and Figures S1, S2(a), S2(b) and S3. 1 MNA Force Field [1] Nonbonded Interactions: 12 πππ π(πππ ) = 4πππ [( ) πππ 6 πππ ππ ππ −( ) ]+ πππ 4ππ0 πππ where πππ is the atom-atom separation distance; πππ , ππ are the Lennard-Jones well depth and diameter, respectively; ππ , ππ are partial charge on π and π , respectively; π0 is permittivity of vacuum. Bond Stretching: πππππ = ππ (π − π0 ) 2 Where ππ is the force constant, π is the current bond length and π0 is the equilibrium bond length. Angle Bending: πππππ = ππ (π − π0 ) 2 Where ππ is the force constant, π is the current bond length and π0 is the equilibrium bond length. Torsion: π ππ‘πππ = ∑ ππ (1 + πππ (ππ − πΏ)) π=1 Where π is the dihedral angle, and ππ are constants. 2 Table 1 Lennard-Jones Parameters for MNA (United Atom) [1]. Parentheses denote functional group attached to the atom of interest. π(π) π(π) π(β«) CH-(aro) 3.74 48 0 C-(NH) 4.50 15 0.187 N-(CH3) 3.52 58 -0.730 H-(N) 0.0 0.0 0.365 CH3 3.75 98 0.234 C-(NO2) 4.50 15 0.131 N-(O) 3.31 40 0.711 O-(N) 2.90 80 -0.449 Note: The partial charges were scaled by a factor of 0.94 in our calculations as used by Sokkalingam et al. [1] in their octanol-water partition coefficient calculation. Site Table 2 Bond Stretching Parameters for MNA. Bond C-C C-NO O-N C-NH N-H N-CH3 Bond length (β«) 1.40 1.45 1.22 1.35 0.99 1.44 ππ ⁄2 (kcal/mol) 529.35 361.61 872.54 528.94 614.35 413.41 Table 3 Bending Parameters for MNA. Bond C-C-C C-C-NO O-N-C O-N-O C-C-NH C-NH-C H-N-CH3 Bond length (degree) 120 120 111.50 125 120 112.9 112.9 3 ππ ⁄2 (kcal/mol) 189.40 154.80 167.90 181.10 145.40 73.90 72.90 Table 4 Torsional Parameters for MNA. Bond C-C-C-C O-N-C-C C-N-C-C π πΏ 2 1,2 2,4 180 180, 180 180, 180 ππ (kcal/mol) 15.230 -0.136, 4.351 3.003, -0.308 0.12 0 .0 0 .0 0 .0 0 .0 Nu 20 9 1 8 1 7 1 6 1 5 1 4 1 m be ro fs 13 2 1 1 1 0 1 9 ub en se o 18 7 6 5 m ble s 4 3 2 ate W 1 no cta l 0 .0 2 8 6 4 Probabilit y of trans itions 0.1 0 0 r Figure S1 Probability distributions as a function of subensemble during the gradual insertion of a single MNA molecule into water and 1-octanol solvents in the EE simulations. 4 0.5 a PP+ Acceptance ratio 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of subensembles 0.5 b PP+ Acceptance ratio 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of subensembles Figure S2 Acceptance ratios of transitions between adjacent subensembles calculated during the (a) hydration free energy calculation in water and (b) solvation free energy simulation in 1octanol using EE algorithm. The acceptance ratio of transitions from mth to (m-1)th subensemble represented by π− and the acceptance ratio of transitions from mth to (m+1)th subensemble represented by π+ . 5 25 20 15 ο¨m and Gm/kT 10 5 0 -5 -10 -15 -20 -25 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ο‘m Figure S3 The changes in free energy, πΊπ ⁄ππ , and balancing factor,ππ , as a function of insertion parameter (πΌπ ) where the subscript π, in all cases, represents the subensemble for which the values are plotted and can be an integer value between 1 and 20. ππ (ο) in the calculation of hydration free energy is compared with πΊπ ⁄ππ (β) during the insertion of MNA in water and ππ (ο) in the calculation of solvation free energy is compared with πΊπ ⁄ππ (---) during the insertion of MNA in 1-octanol. 6 References 1. N. Sokkalingam, M . H. Ketko and J. J. Potoff , “Physical property prediction of energetic materials from molecular dynamics simulation”, a chapter in Energetic Materials: Thermophysical properties, Predictions and Experimental Measurements edited by V. Boddu and P. Redner (CRC Press, Boca Raton, 2010). 7